My teacher told me that usually we can't reduce vectors for example (6,8) can't be reduced to (3,4) but she also said that sometimes we can reduce. Can somebody please explain to me when we can and can't reduce vectors and why?

Thank you

You can reduce when all you care about is the direction. If you reduce than the magnitude is not preserved
.

All right but then in what case would you not care about magnitude at all and just want the direction?